Assets, Beliefs, and Equilibria in Economic Dynamics

This collection of papers is dedicated to Mordecai Kurz — our friend, mentor, and colleague. They are to mark our appreciation of his contributions to economic science, from which we have all benefited enormously. A conference in his honor took place on August 2–3, 2002, co-hosted by the Stanford University Department of Economics, the Stanford Institute of Economic Policy Research, and Springer-Verlag. At this conference a selection of these papers was presented, along with some more recent work by several of the same authors and by other invitees.

In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism.

This paper attempts to circumvent the nonsense of the representative agent which arises in macroeconomics. It recognises that macro data are relevant to agents’ decisions, and so excess demands should contain macro variables as arguments. The macro variables I consider are the price index, unemployment and GNP. This paper should be regarded as a tentative beginning to make macroeconomic theory literate.

Evidence is adduced that the sages of the ancient Babylonian Talmud, as well as some of the medieval commentators thereon, were well aware of sophisticated concepts of modern theories of risk-bearing.

This paper examines the interaction between the market for annuities and retirement and consumption decisions in the presence of lifetime uncertainty. We focus on two aspects of the demand for annuities: the timingof annuitization and the information available to the issuers of annuities with regard to purchasers’ survival probabilities. The First-Best is attained by continuous annuitization of savings, with a guaranteed lump-sum payment to beneficiaries upon death. Annuitization of savings at retirement, and a-fortioti no annuitization, are inferior and lead to distortions in retirement and consumption decisions. Applying a ‘Stochastic Dominance’ approach, we show how these decisions depend on individuals’ degree of risk aversion. Under imperfect information, we analyze Pooling Equilibria and compare them with the First-Best.

We investigate the existence of consistent rules for the resolution of conflicting claims that generalize the Talmud rule but do not necessarily satisfy equal treatment of equal. The first approach we follow starts from the description of the Talmud rule in the two-claimant case as “concede-and-divide”, and an axiomatic characterization for the rule. When equal treatment of equals is dropped, we obtain a one-parameter family, “weighted concede-and-divide rules”. The second approach starts from the description of the Talmud rule as a hybrid of the constrained equal awards and constrained equal losses rules, and weighted generalizations of these rules. We characterize the class of consistent rules that coincide with weighted concede-and-divide rules in the two-claimant case or with weighted hybrid rules. They are defined by partitioning the set of potential claimants into “priority classes” or “half-priority classes” respectively, and selecting reference weights for all potential claimants. For the first approach however, and in each class with more than two claimants, equal treatment is actually required

This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions.

Using the concept of ex-post optimality, we compare different exchange rate regimes, including floating exchange rates and fixed exchange rates with a Monetary Union in a two country OLG model with stochastic endowments. The emphasis of this comparison is on the welfare consequences of agents having incorrect beliefs. We do not assume that agents can hold any beliefs, but rather that their beliefs are rational that is consistent with the observed empirical behavior of the economy. We study a large set of possible policies, but two of them have our particular interest. The first policy implies devaluations in reaction to a negative shock, while the other implies a fixed exchange rate. These policies have very different consequences. The first will for generic beliefs not result in an ex-post optimal allocation. The other policy is on the other hand always feasible and results in an ex-post optimal allocation. When the two countries form a Monetary Union, the expost optimal allocation is also achieved. The meaning of “endogenous uncertainty” as an institutionally induced uncertainty is illustrated.

We study some implications of the Theory of Rational Beliefs to monetary policy. We show that monetary policy in a Rational Beliefs environment can have an important effect on the characteristics of economic fluctuations. In Rational Beliefs Equilibria money is genetically non-neutral unlike Rational Expectations Equilibria in which money is neutral and monetary policy is ineffective. Under Rational Beliefs Equilibria nominal prices and real output change not only in response to changes in the exogenous growth rate of money but also in response to changes in the state of beliefs. In Rational Beliefs Equilibria monetary shocks have real effects even when they are observed but are not fully anticipated. Furthermore, the non-neutrality of money results in a short run Phillips curve. When money “flutters, real output sputters” [8]. We show that Endogenous Uncertainty and the distribution of market beliefs are the major explanatory variables of such fluctuations. Under Rational Expectations monetary policy is ineffective because agents neutralize it by predicting correctly the effect of the policy. Under Rational Beliefs it is shown instead that inflation and recessions can be substantially aggravated by the distribution of market beliefs.

We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes’ general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). At the other extreme, if the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual.

The present paper is an extension of Ghiglino and Shell [7] to the case of imperfect consumer credit markets. We show that with constraints on individual credit and only anonymous (i.e., non-personalized) lump-sum taxes, strong (or “global”) irrelevance of government budget deficits is not possible, and weak (or “local”) irrelevance can hold only in very special situations. This is in sharp contrast to the result for perfect credit markets. With credit constraints and anonymous consumption taxes, weak irrelevance holds if the number of tax instruments is sufficiently large and at least one consumer’s credit constraint is not binding. This is an extension of the result for perfect credit markets.

In this paper I consider a dynamically complete market model without intrinsic uncertainty. Agents’ beliefs are different, but correct in the limit. Some agents are more patient than others. I show that infinitely often share prices are low and the economy stagnates. Also, infinitely often share prices are high and the economy grows. The changes from growth to stagnation and from stagnation to growth are not caused by exogenous shocks. They are caused by speculative trade among agents with different propensities to save and invest.

This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods, and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either autarchy or the stochastic analogue of the Golden Rule.

The monetary character of trade, use of a common medium of exchange, is shown to be an outcome of economic general equilibrium in the presence of transaction costs and market segmentation (in trading posts with a separate budget constraint at each transaction). Commodity money arises endogenously as the most liquid (lowest transaction cost) asset. Scale economies in transaction cost account for uniqueness of the (fiat or commodity) money in equilibrium, creating a natural monopoly. Trading posts using a medium of exchange create a network externality inducing others’ adoption of the same medium. Bertrand monetary equilibria (among competing trading posts) and uniqueness of ‘money’ are robust to threats of entry. Government-issued fiat money has a positive equilibrium value from its acceptability for tax payments and sustains its natural monopoly through the scale of government economic activity.

This paper develops some general conditions under which complementarities between individual agents imply that assortative matching is efficient. Our analysis has four main findings. First, when agents are organized into equal-sized groups, just as in Becker (1973), the presence of within-group complementarities is sufficient for stratification to be efficient. Second, if group sizes vary, assortative matching may not be efficient even though complementarities are present, unless particular functional form assumptions are imposed. Third, the connection between assortative matching, complementarities and efficiency reemerges if one considers sequences of replications of the economy in which individual coalitions are uniformly bounded in size. Fourth, the presence of feedbacks from the composition of group memberships has important effects on efficient allocations and breaks any simple link between assortative matching and efficiency. Together, these results suggest that the characterization of the cross-section evolution of an efficiently sorted economy is likely to be highly complex.

In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered.

We generalize the Vickrey auction to allow for reserve pricing in a multi-unit auction with interdependent values. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders’ reports of private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings with perfect resale, the Vickrey auction with reserve pricing maximizes seller revenues.

This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players’ strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core.

Investors often wish to insure themselves against the payoff of their portfolios falling below a certain value. One way of doing this is by purchasing an appropriate collection of traded securities. However, when the derivatives market is not complete, an investor who seeks portfolio insurance will also be interested in the cheapest hedge that is marketed. Such insurance will not exactly replicate the desired insured-payoff, but it is the cheapest that can be achieved using the market. Analytically, the problem of finding a cheapest insuring portfolio is a linear programming problem. The present paper provides an alternative portfolio dominance approach to solving the minimum-premium insurance portfolio problem. This affords remarkably rich and intuitive insights to determining and describing the minimum-premium insurance portfolios.

This paper obtains finite counterparts of previous results that showed the informational efficiency of the Walrasian mechanism among all mechanisms yielding Pareto-optimal individually rational trades in exchange economies while using a continuum of possible messages. Such “continuum” mechanisms lack realism, even when the space of environments (characteristics) is a continuum, since it is not possible to transmit or announce all elements of a message continuum, and it generally takes infinite time to find an exact equilibrium message among all messages in such a continuum. Accordingly the paper studies finite approximations (having a finite number of messages) of the continuum Walrasian mechanism and of other continuum allocation mechanisms. An approximation’s overall error for a class of exchange economies, is the largest distance, over all economies in the class, between the continuum mechanism’s final allocation and the approximation’s final allocation. In particular, we develop finite counterpart s of the superiority, with respect to message-space dimension, of the Walrasian mechanism over Direct Revelation (DR). We measure a finite mechanism’s cost by the number of its (equilibrium) messages.Our two main results are as follows: (1) For exchange economies we find that the overall error of a (sufficiently fine) approximate Walrasian mechanism is less than the overall error of a not-more-costly approximation of a continuum DR mechanism whose equilibrium outcomes are trades that are Pareto optimal and individually rational. More generally, approximate Walrasian mechanisms are superior, in the same sense, to approximations of any continuum mechanism whose equilibrium outcomes (like those of the continuum Walrasian mechanism) are Pareto optimal individually rational trades and whose message space has higher dimension than that of the Walrasian mechanism. (2) As we increase without limit the dimension of the set of environments (characteristics) defining our class of exchange economies, we find that the extra cost of such DR approximations relative to Walrasian approximations, when both achieve the same overall error, also grows without limit.Thus the informational superiority of the Walrasian mechanism emerges again when we approximate it and take the finite number of messages in the approximation as our cost measure.

In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation.

The existence of Nash and Walras equilibrium is proved via Brouwer’s Fixed Point Theorem, without recourse to Kakutani’s Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.”

This paper analyzes the applicability of CVM (Contingent Valuation Method) for the economic assessment of the tele-health system. By focusing on the discrepancy between WTP (Willingness to pay) and WTA (Willingness to accept), we decompose the discrepancy into income and endowment effect according to the method used by Morrison [21, 22]. We also closely examine the endowment effect, and break it down into several components. It is noted that the portion, which was thought to be the endowment effect, contains imaginary as well as subsidy biases, and the endowment effect is not as large as previously estimated.

We give a geometric interpretation of the lens condition, proposed by Deardorff as a shortcut for checking the factor price equalization (FPE) condition. We identify the conditions under which the lens condition implies the FPE condition. If the FPE zone is not a neighborhood of the diagonal allocations, however, the lens condition is irrelevant despite the implication since the FPE condition (hence the lens condition) is unlikely to be satisfied in that case. We give precise conditions under which the lens condition is equivalent to the FPE condition and simultaneously, the FPE zone is a neighborhood of the diagonal allocations.

In this paper, we establish the most possilbe general formulation of the technology governing carbon-gas emission, giving rise to global external diseconomies, and ty to explore into the strategic interactions,both domestic and international, when an individual country decides on the environmental policies. Through the comparison among emission taxes, quotas, and standard in the perfectly competitive private economies, we find that the first two policies are equivalent but they are different in effects by virtue of what we may call the tax-exemption effect of emission standards. Such a difference in the policy effect further affects the other country’s welfare through the global externalities, amplified through whether the government can precommit to either the emission tax or the emission standard.

An adverse selection model of firm reputation is developed in which short-lived clients purchase services from firms operated by overlapping generations of agents. A firm’s only asset is its name, or reputation, and trade of names is not observed by clients. As a result, names are traded in all equilibria regardless of the economy’s horizon The general equilibrium analysis links the value of a name to the market for services. This causes a non-monotonicity that precludes higher types from sorting themselves through the market for names, and leads to “sensible” dynamics: reputations, and name prices, increase after success and decrease after failure.

In this paper we look at the empirical evidence in favor of structural breaks in the conditional volatility of some important macroeconomic and financial time series like currency returns, stock returns, output and inflation. We find strong evidence of both structural breaks and long memory in the break-free series. We use a variety of econometric methodologies, both parametric and non-parametric, in order to verify the robustness of our findings, which provide strong empirical evidence in favor of the Theory of Rational Beliefs.

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition.

The age-old concept of allocating scarce resources according to “relative need” has proven notoriously difficult to formalize in a rigorous manner. This paper presents a new solution concept for this classical problem. After first providing a formal definition of what it means for one agent to be “everywhere needier than” another, we prove that the condition of being “needier than” is equivalent to being “more risk averse than”. Next, we introduce and axiomatize a scalar measure of “relative neediness”. This measure then becomes the basis for a needs-based allocation rule applicable to general n-person arbitration problems. The resulting allocation rule is closely related to the Nash bargaining solution, and does not entail explicit interpersonal comparisons of utility. In the final section, the new solution concept is embedded within a comprehensive theory of distributive justice.

We examine a multistage model of an R&D race where players have multiple projects. We also develop perturbation methods for general dynamic games that can be expressed as analytic operators in a Banach space. We apply these perturbation methods to solve races with a small prize. We compute second-order asymptotically valid solutions for equilibrium and socially optimal decisions to determine qualitative properties of equilibrium. We find that innovators invest relatively too much on risky projects. Strategic reactions are ambiguous in general; in particular, a player may increase expenditures as his opponent moves ahead of him.

This paper studies how communication or exchange of opinions influences correlation of beliefs. The paper focuses on a situation in which agents communicate with each other infinitely many times without observing data. It is an extension to the ‘Expert Problem’ in Bayesian theory, where the informational flow is asymmetric. Moreover, this paper generalizes the existing literature of communication that employs the common prior assumption (CPA) by allowing for heterogeneous beliefs. Some basic convergence results are shown in contrast with the results obtained under the CPA. Furthermore, several economic implications of the basic results are provided.

We quantitatively explore how asset market structure affects risk-sharing, welfare, and trading volume in stylized rational expectations models. We examine five market structures: perfect asset trading, only bonds and equity, only equity, only bonds, and autarchy. We find a variety of results. First, trade in a single asset, either bond or stock, achieves most of the utility gain from going to perfect markets. Second, the value of adding a bond (stock) to the stock (bond) only economy is generally quite small, and has negligible price effects. Third, even in our simple model, the addition of a new asset may harm many traders. Fourth, adding a new asset may increase trading volume in old assets. Fifth, completing the market beyond a stock and bond may have substantial price and welfare effects, indicating that adding assets like options can have significant economic effects.

Let % MathType!MTEF!2!1!+-% feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiWaaeaaca% WGybWaaSbaaSqaaiaadQgaaeqaaaGccaGL7bGaayzFaaWaa0baaSqa% aiaaicdaaeaacqGHEisPaaaaaa!3C7E!$$ \left\{ {{X_j}} \right\}_0^\infty $$ be a Markov chain with a unique stationary distribution π. Let h be a bounded measurable function. Write % MathType!MTEF!2!1!+-% feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdW2aaS% baaSqaaiaadIgaaeqaaOGaeyypa0Zaa8qaaeaacaWGObGaamizaiab% ec8aWbWcbeqab0Gaey4kIipaaaa!3F5E!$$ {\lambda _h} = \int {hd\pi } $$ and % MathType!MTEF!2!1!+-% feaaguart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4UdWMbaK% aadaWgaaWcbaGaamiAaiaad6gaaeqaaOGaeyypa0ZaaSaaaeaacaaI% XaaabaWaaeWaaeaacaWGUbGaey4kaSIaaGymaaGaayjkaiaawMcaaa% aadaaeWaqaaiaadIgadaqadaqaaiaadIfadaWgaaWcbaGaamOAaaqa% baaakiaawIcacaGLPaaaaSqaaiaaicdaaeaacaWGUbaaniabggHiLd% aaaa!47DE!$$ {\hat \lambda _{hn}} = \frac{1}{{\left( {n + 1} \right)}}\sum\nolimits_0^n {h\left( {{X_j}} \right)} $$. This paper explores conditions for the √n consistency and asymptotic normality of the estimate of λ̂hn of λh assuming the existence of a solution to the Poisson equation h - λh = g - Pg. Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics.

Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo σ -algebra, which represents macroeconomic risk, individual agents’ random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved.

The analysis of the demand for insurance has been significantly affected by the failure to recognize the composite commodity theorem. This fact is demonstrated when the composite commodity theorem is used to modify the existing model so that insurance demand is more appropriately calculated. Comparative static properties of the modified model are derived and more reasonable comparative static results are obtained. Most importantly, in the modified model increases in wealth need not lead to a reduction in the quantity of insurance demanded even for decreasing absolute risk averse decision makers.